with {Mk} defined as

5) Let {Xk}k=1n be a sequence of independent random variables where the distribution of each r.v. Xk is given by P(Xk=1)=P(Xk=1)=1/2 (thus, we have a model of a sequence of independent tosses of a fair coin). Define {Mk}k=0n as in Question 2. Let be real. Compute, for k1,E[eMkFk1]. Hence, find a martingale involving eMk. M0=1, and Mk=i=1kXi,k1 5) Let {Xk}k=1n be a sequence of independent random variables where the distribution of each r.v. Xk is given by P(Xk=1)=P(Xk=1)=1/2 (thus, we have a model of a sequence of independent tosses of a fair coin). Define {Mk}k=0n as in Question 2. Let be real. Compute, for k1,E[eMkFk1]. Hence, find a martingale involving eMk. M0=1, and Mk=i=1kXi,k1